This paper addresses the difficult problem of selecting representative samples of peer properties (e.g., degree, link bandwidth, number of files shared) in unstructured peer-to-peer systems. Due to the large size and dynamic nature of these systems, measuring the quantities of interest on every peer is often prohibitively expensive, while sampling provides a natural means for estimating system-wide behavior efficiently. However, commonly-used sampling techniques for measuring peer-to-peer systems tend to introduce considerable bias for two reasons. First, the dynamic nature of peers can bias results towards short-lived peers, much as naively sampling flows in a router can lead to bias towards short-lived flows. Second, the heterogeneous nature of the overlay topology can lead to bias towards high-degree peers. We present a detailed examination of the ways that the behavior of peer-to-peer systems can introduce bias and suggest the Metropolized Random Walk with Backtracking (MRWB) as a viable and promising technique for collecting nearly unbiased samples. We conduct an extensive simulation study to demonstrate that the proposed technique works well for a wide variety of common peer-to-peer network conditions. Using the Gnutella network, we empirically show that our implementation of the MRWB technique yields more accurate samples than relying on commonlyused sampling techniques. Furthermore, we provide insights into the causes of the observed differences. The tool we have developed, ion-sampler, selects peer addresses uniformly at random using the MRWB technique. These addresses may then be used as input to another measurement tool to collect data on a particular property.

Accurate measurement, inference and modelling techniques are fundamental to Internet topology research. Spatial analysis of the Internet is needed to develop network planning, optimal routing algorithms and failure detection measures. A first step towards achieving such goals is the availability of network topologies at different levels of granularity, facilitating realistic simulations of new Internet systems. The main objective of this survey is to familiarize the reader with research on network topology over the past decade. We study techniques for inference, modelling and generation of the Internet topology at both router and administrative level. We also compare the mathematical models assigned to various topologies and the generation tools based on them. We conclude with a look at emerging areas of research and potential future research directions.

Abstract — Peer-to-peer systems are becoming increasingly popular, with millions of simultaneous users and a wide range of applications. Understanding existing systems and devising new peer-to-peer techniques relies on access to representative models derived from empirical observations. Due to the large and dynamic nature of these systems, directly capturing global behavior is often impractical. Sampling is a natural approach for learning about these systems, and most previous studies rely on it to collect data. This paper addresses the common problem of selecting representative samples of peer properties such as peer degree, link bandwidth, or the number of files shared. A good sampling technique will select any of the peers present with equal probability. However, common sampling techniques introduce bias in two ways. First, the dynamic nature of peers can bias results towards short-lived peers, much as naively sampling flows in a router can lead to bias towards short-lived flows. Second, the heterogeneous overlay topology can lead to bias towards high-degree peers. We present preliminary evidence suggesting that applying a degreecorrection method to random walk-based peer selection leads to unbiased sampling, at the expense of a loss of efficiency. I.

In this paper, we develop methods to ‘‘sample’ ’ a small realistic graph from a large Internet topology. Despite recent activity, modeling and generation of realistic graphs resembling the Internet is still not a resolved issue. All previous work has attempted to grow such graphs from scratch. We address the complementary problem of shrinking an existing topology. In more detail, this work has three parts. First, we propose a number of reduction methods that can be categorized into three classes: (a) deletion methods, (b) contraction methods, and (c) exploration methods. We prove that some of them maintain key properties of the initial graph. We implement our methods and show that we can effectively reduce the nodes of an Internet graph by as much as 70 % while maintaining its important properties. Second, we show that our reduced graphs compare favorably against construction-based generators. Finally, we successfully validate the effectiveness of our best methods in an actual performance evaluation study of multicast routing. Apart from its practical applications, the problem of graph sampling is of independent interest.

Abstract—The Internet community has not reached a consensus on an appropriate topological model for evaluating the performance of inter-domain routing protocols. Using the current Internet topology is not realistic, since its size is prohibitively large for, say, a packet-level BGP simulation. Furthermore, routing policies, which play a critical role in inter-domain routing, are often ignored in many simulation studies. In this paper, we address this issue by designing an algorithm to generate small-scale, realistic, and policy-aware topologies. We propose HBR, a network sampling method, which produces topologies that preserve the fundamental properties of the Internet graph, including, in particular, its hierarchical structure. Our approach provides a long-term solution to the difficult problem of AS-level routing evaluations: it can be used to generate small realistic topologies in the future, starting from any newer or more complete Internet instance. I.

Abstract. We put forward a zero-knowledge based definition of privacy. Our notion is strictly stronger than the notion of differential privacy and is particularly attractive when modeling privacy in social networks. We furthermore demonstrate that it can be meaningfully achieved for tasks such as computing averages, fractions, histograms, and a variety of graph parameters and properties, such as average degree and distance to connectivity. Our results are obtained by establishing a connection between zero-knowledge privacy and sample complexity, and by leveraging recent sublinear time algorithms. 1

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Abstract — A major challenge that researchers face in studying Denial of service (DoS) attacks is the size of the network to be investigated. A typical DoS attack usually takes place over a large portion of the Internet and involves a considerable number of hosts. This can be intractable for testbed experimentation, and even simulation. Therefore, it is important to simplify a network scenario with DoS attacks before applying it to a simulation/testbed platform. Several approaches have been proposed in the literature to downscale a network scenario, while preserving certain critical properties. In this paper, we investigate via simulations the applicability of packet-level downscaling approaches to DoS scenarios. We select two representative methods: SHRiNK and TranSim. Our experiments identify the operational range of the two downscaling approaches, and propose guidelines for researches to select the most suitable downscaling approach for their own research. I.

Given a huge real graph, how can we derive a representative sample? There are many known algorithms to compute interesting measures (shortest paths, centrality, betweenness, etc.), but several of them become impractical for large graphs. Thus graph sampling is essential.

Is approved by the final examining committee: